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Q.

The population of a city is 125000. If the annual birth rate and death rate are $5.5 %$ and $3.5 %$ respectively, calculate the population of city after 3 years.

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a

132651

b

137651

c

162651

d

532651

answer is A.

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Detailed Solution

Given,
Initial population of a city, P=125000,
Rate of growth of population, R=2% ,
Number of years, n=3.
If P is the population of a city at the beginning of specific year and R% is its constant growth rate per annum, we use the following formula to calculate the population after n years:
Population after n years

= P 1 + R 100 n

Annual birth rate =5.5%
Annual death rate =3.5%
Therefore, annual growth rate is (5.5-3.5)% = 2%.
Population of a city after 3 years

= P 1 + R 100 n

⇒ 125000 1 + 2100 3 ⇒ 125000 1.02 3 ⇒ 125000 × 1.061208 ⇒ 132651

Hence, the population of a city after 3 years will be 132651.
Therefore, option (1) is correct.

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